Since joining the club in July 2011, the Ivory Coast international has struggled to establish himself as a regular first-team player under Arsene Wenger, making just 19 starts in his first season.
The 25-year-old started this campaign on a brighter note, netting five goals in Arsenal's opening seven matches, but a dip in form has seen the forward lose his place to Theo Walcott.
"I'm in one of the best clubs in the world. I've got one of the best managers in the world. I've always wanted to be here. I think long-term, not short-term," he told Goal.com.
"I want to be here for a long time, do better than all the other players that came here in the past. I'm not thinking about going somewhere else for the moment. But to mention the club and the fans, you never know, but for the moment I'm here for a long-term stay."
Arsenal has struggled for consistent form this season and currently sits sixth in the Premier League table, 21 points behind leader Manchester United, but Gervinho insists that the feeling at the club remains positive.
"It's never easy when your team is having a hard time," Gervinho said. "We try not to think about it too much after every game when things are bad. We are responsible for whatever happens to the club. The atmosphere in the locker room is good. We try to keep our heads cool and our chins up to win every weekend.
"Sometimes it works better than others but you have to focus on the positive side so for that next game you still have the right state of mind. We've been through some tough periods in the league, but every time we have managed to come back stronger and give our best."
The 25-year-old also praised the passion shown from fans in English football, since his 10 million pound move from Lille 18 months ago.
"The passion the British people have for football... they live for football," he said. "Whatever difficulty their club is having the supporters are always behind it, they don't give up, they travel away with the team. My most striking image is this passion people have for football."